What principal amount will yield simple interest of Rs. 120 at a rate of 6% per annum over a period of 10 years, assuming interest is calculated using the simple interest formula?

Introduction / Context:
This question is a basic reverse simple interest calculation. We know the interest earned, the rate of interest, and the time period, and we are asked to find the principal that produces that interest. Such questions are straightforward but essential building blocks for more complex financial reasoning. Understanding how to isolate principal in the simple interest formula is crucial.

Given Data / Assumptions:
Simple interest I is Rs. 120.
Rate of interest r is 6 percent per annum.
Time period t is 10 years.
Principal P is unknown.
Interest is simple interest with a constant rate each year.

Concept / Approach:
The simple interest formula is I = P * r * t / 100. When I, r, and t are given, we can rearrange the formula to solve for the principal as P = I * 100 / (r * t). Substituting the known values yields the principal that would generate the given interest under the stated conditions. This is a direct algebraic manipulation of the formula.

Step-by-Step Solution:
Start from the simple interest formula I = P * r * t / 100.Substitute I = 120, r = 6, and t = 10.So 120 = P * 6 * 10 / 100.Compute 6 * 10 = 60, so the equation becomes 120 = P * 60 / 100.Simplify 60 / 100 to 0.6, so 120 = 0.6P.Solve for P by dividing both sides by 0.6: P = 120 / 0.6 = 200.Therefore the principal amount is Rs. 200.

Verification / Alternative check:
Check by computing simple interest on Rs. 200 at 6 percent per annum for 10 years. Interest I equals 200 * 6 * 10 / 100 = 200 * 60 / 100 = 120 rupees. This matches the interest given in the problem, confirming that Rs. 200 is the correct principal.

Why Other Options Are Wrong:
Rs. 120 would give interest of 120 * 6 * 10 / 100 = 72 rupees, which is less than 120 rupees.
Rs. 180 would produce interest of 108 rupees, still not equal to 120 rupees.
Rs. 210 would give 126 rupees interest, which is slightly higher than 120 rupees.
Rs. 240 would yield 144 rupees interest, which is too high. Thus only Rs. 200 yields exactly Rs. 120 as simple interest under the given conditions.

Common Pitfalls:
Common mistakes include misplacing the 100 factor in the formula or forgetting to multiply both rate and time before dividing. Some learners also confuse interest with amount and attempt to subtract or add values unnecessarily. Writing the rearranged formula for principal explicitly and then plugging in the numbers helps avoid such confusion.

Final Answer:
The principal that yields simple interest of Rs. 120 at 6 percent per annum in 10 years is Rs. 200.